One of my favorite 'fantasy' characters is Uhtred of Bebbanburg from Bernard Cornwell's Saxon stories. I want to be a warlord like that, so I dish out loot to my followers in the manner of early feudal warbands. I tried to buy a spare horse for one, but is that possible? How do I get them to ride it? I want to be a gift-giver so men will respect me!

^{They can't ride it, the only option for them to interact with it is to attack it.}

The only way for a follower to ride is to have a horse available to them, and a script which checks if the player is riding with the condition the NPC is following, if the player is riding it has the NPC mount up, if the player is not riding, they dismount.
These checks need to fire pretty much all the time too.

Take a look at the Stoker mod for Oblivion in the TES IV editor for a good example of this.